Geometric properties of the shifted hypergeometric functions

2017/04/26 by Sugawa, Toshiyuki, Wang, Li-Mei
#Complex Variables (math.CV) #FOS: Mathematics #Primary 30C45 #Secondary 33C05

paper · doi:10.48550/arxiv.1704.07948

Abstract

We will provide sufficient conditions for the shifted hypergeometric function z₂F₁(a,b;c;z) to be a member of a specific subclass of starlike functions in terms of the complex parameters a,b and c. For example, we study starlikeness of order α, λ-spirallikeness of order α and strong starlikeness of order α. In particular, those properties lead to univalence of the shifted hypergeometric functions on the unit disk.

Related

• Spirallikeness of shifted hypergeometric functions
• A generalization of starlike functions of order alpha
• Radius of starlikeness for some classes containing non-univalent functions
• Geometric properties of a certain class of functions related to the Fox-Wright functions
• On a generalization of starlike functions